Question : In a triangle ABC, the three angles are $x, y$, and $y+10$. Also, $2x-4y=20^{\circ}$. Which type of triangle is ABC?
Option 1: Equilateral
Option 2: Obtuse
Option 3: Acute
Option 4: Right-angled
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Correct Answer: Right-angled
Solution :
In a triangle ABC, the three angles are $x,y$, and $y+10$.
Also, $2x-4y=20^{\circ}$
The sum of all angles of a triangle is $180^\circ$
$\therefore$ $x+y+y+10=180^{\circ}$
⇒ $x+2y = 170^{\circ}$.............(1)
Given that, $2x-4y=20^{\circ}$.........(2)
Solving the above two equations by performing 2(equation 1) + (equation 2), we get:
$4x=360^\circ$
⇒ $x=90^{\circ}$
⇒ The triangle ABC is right-angled.
Hence, the correct answer is Right-angled.
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